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The boxes are now filled. So,
start adding from right to left.
In case, the sum is a two-digit Tips
7
number, add the tens digit to
the sum of the next diagonal. In the lattice method, the
final product is obtained by
adding the numbers along
the diagonals, starting from
the bottom right.
In the first diagonal, sum = 2
Sum of numbers in the second diagonal = 6 + 4 + 6 = 16
4+ 1 =5 Write 6 and carry over 1 to the sum of the next diagonal.
3+8+5+1= 1 7 Sum of numbers in the third diagonal = 3 + 8 + 5 + 1 (carry over) = 17
6+4+6= 1 6
Write 7 and add 1 to the next diagonal = 4 + 1 (carry over) = 5.
Read the sums of the diagonals from left to right to get the final
product.
Thus, 86 × 67 = 5762.
Multiplication by 10 and its Multiples
When a number is multiplied by 10, we put a zero to the right of the number.
Examples: a. 342 × 10 = 3420 b. 5648 × 10 = 56480
When a number is multiplied by 20, 30, 40, ..., 90, we multiply the number by
2, 3, 4, ..., 9 respectively and put a zero to the right of the product so obtained.
Examples: a. 278 × 20 = 5560 b. 3142 × 50 = 157100
When a number is multiplied by 100, we put two zeros to the right of the number.
Examples: a. 643 × 100 = 64300 b. 8572 × 100 = 857200
When a number is multiplied by 200, 300, 400, ..., 900, we multiply the number
by 2, 3, 4, ..., 9 respectively and then put two zeros to the right of the product so
obtained.
Examples: a. 78 × 400 = 31200 b. 273 × 800 = 218400
When a number is multiplied by 1000, we put three zeros to the right of the number.
Examples: a. 15 × 1000 = 15000 b. 198 × 1000 = 198000
When a number is multiplied by 2000, 3000, 4000, ..., 9000, we multiply the
number by 2, 3, 4, ..., 9 respectively and then put three zeros to the right of the
product so obtained.
Examples: a. 24 × 3000 = 72000 b. 571 × 7000 = 3997000
48 Mathematics 5
